#include "iwavl.h"

/*
 * avl_tree.c - intrusive, nonrecursive AVL tree data structure (self-balancing
 *		binary search tree), implementation file
 *
 * Written in 2014-2016 by Eric Biggers <ebiggers3@gmail.com>
 *
 * To the extent possible under law, the author(s) have dedicated all copyright
 * and related and neighboring rights to this software to the public domain
 * worldwide via the Creative Commons Zero 1.0 Universal Public Domain
 * Dedication (the "CC0").
 *
 * This software is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE. See the CC0 for more details.
 *
 * You should have received a copy of the CC0 along with this software; if not
 * see <http://creativecommons.org/publicdomain/zero/1.0/>.
 */


/* Returns the left child (sign < 0) or the right child (sign > 0) of the
 * specified AVL tree node.
 * Note: for all calls of this, 'sign' is constant at compilation time,
 * so the compiler can remove the conditional.  */
IW_INLINE struct iwavl_node* iwavl_get_child(const struct iwavl_node *parent, int sign) {
  if (sign < 0) {
    return parent->left;
  } else {
    return parent->right;
  }
}

IW_INLINE struct iwavl_node* iwavl_first_or_last_in_order(const struct iwavl_node *root, int sign) {
  const struct iwavl_node *first = root;

  if (first) {
    while (iwavl_get_child(first, +sign)) {
      first = iwavl_get_child(first, +sign);
    }
  }
  return (struct iwavl_node*) first;
}

/* Starts an in-order traversal of the tree: returns the least-valued node, or
 * 0 if the tree is empty.  */
struct iwavl_node* iwavl_first_in_order(const struct iwavl_node *root) {
  return iwavl_first_or_last_in_order(root, -1);
}

/* Starts a *reverse* in-order traversal of the tree: returns the
 * greatest-valued node, or 0 if the tree is empty.  */
struct iwavl_node* iwavl_last_in_order(const struct iwavl_node *root) {
  return iwavl_first_or_last_in_order(root, 1);
}

IW_INLINE struct iwavl_node* iwavl_next_or_prev_in_order(const struct iwavl_node *node, int sign) {
  const struct iwavl_node *next;

  if (iwavl_get_child(node, +sign)) {
    for (next = iwavl_get_child(node, +sign);
         iwavl_get_child(next, -sign);
         next = iwavl_get_child(next, -sign)) {
      ;
    }
  } else {
    for (next = iwavl_get_parent(node);
         next && node == iwavl_get_child(next, +sign);
         node = next, next = iwavl_get_parent(next)) {
      ;
    }
  }
  return (struct iwavl_node*) next;
}

/* Continues an in-order traversal of the tree: returns the next-greatest-valued
 * node, or 0 if there is none.  */
struct iwavl_node* iwavl_next_in_order(const struct iwavl_node *node) {
  return iwavl_next_or_prev_in_order(node, 1);
}

/* Continues a *reverse* in-order traversal of the tree: returns the
 * previous-greatest-valued node, or 0 if there is none.  */
struct iwavl_node* iwavl_prev_in_order(const struct iwavl_node *node) {
  return iwavl_next_or_prev_in_order(node, -1);
}

/* Starts a postorder traversal of the tree.  */
struct iwavl_node* iwavl_first_in_postorder(const struct iwavl_node *root) {
  const struct iwavl_node *first = root;

  if (first) {
    while (first->left || first->right) {
      first = first->left ? first->left : first->right;
    }
  }

  return (struct iwavl_node*) first;
}

/* Continues a postorder traversal of the tree.  @prev will not be deferenced as
 * it's allowed that its memory has been freed; @prev_parent must be its saved
 * parent node.  Returns 0 if there are no more nodes (i.e. @prev was the
 * root of the tree).  */
struct iwavl_node* iwavl_next_in_postorder(
  const struct iwavl_node *prev,
  const struct iwavl_node *prev_parent
  ) {
  const struct iwavl_node *next = prev_parent;

  if (next && prev == next->left && next->right) {
    for (next = next->right;
         next->left || next->right;
         next = next->left ? next->left : next->right) {
      ;
    }
  }
  return (struct iwavl_node*) next;
}

/* Sets the left child (sign < 0) or the right child (sign > 0) of the
 * specified AVL tree node.
 * Note: for all calls of this, 'sign' is constant at compilation time,
 * so the compiler can remove the conditional.  */
IW_INLINE void avl_set_child(
  struct iwavl_node *parent, int sign,
  struct iwavl_node *child
  ) {
  if (sign < 0) {
    parent->left = child;
  } else {
    parent->right = child;
  }
}

/* Sets the parent and balance factor of the specified AVL tree node.  */
IW_INLINE void avl_set_parent_balance(
  struct iwavl_node *node, struct iwavl_node *parent,
  int balance_factor
  ) {
  node->parent_balance = (uintptr_t) parent | (balance_factor + 1);
}

/* Sets the parent of the specified AVL tree node.  */
IW_INLINE void avl_set_parent(struct iwavl_node *node, struct iwavl_node *parent) {
  node->parent_balance = (uintptr_t) parent | (node->parent_balance & 3);
}

/* Returns the balance factor of the specified AVL tree node --- that is, the
 * height of its right subtree minus the height of its left subtree.  */
IW_INLINE int avl_get_balance_factor(const struct iwavl_node *node) {
  return (int) (node->parent_balance & 3) - 1;
}

/* Adds @amount to the balance factor of the specified AVL tree node.
 * The caller must ensure this still results in a valid balance factor
 * (-1, 0, or 1).  */
IW_INLINE void avl_adjust_balance_factor(struct iwavl_node *node, int amount) {
  node->parent_balance += amount;
}

IW_INLINE void avl_replace_child(
  struct iwavl_node **root_ptr,
  struct iwavl_node  *parent,
  struct iwavl_node  *old_child,
  struct iwavl_node  *new_child
  ) {
  if (parent) {
    if (old_child == parent->left) {
      parent->left = new_child;
    } else {
      parent->right = new_child;
    }
  } else {
    *root_ptr = new_child;
  }
}

/*
 * Template for performing a single rotation ---
 *
 * sign > 0:  Rotate clockwise (right) rooted at A:
 *
 *           P?            P?
 *           |             |
 *           A             B
 *          / \           / \
 *         B   C?  =>    D?  A
 *        / \               / \
 *       D?  E?            E?  C?
 *
 * (nodes marked with ? may not exist)
 *
 * sign < 0:  Rotate counterclockwise (left) rooted at A:
 *
 *           P?            P?
 *           |             |
 *           A             B
 *          / \           / \
 *         C?  B   =>    A   D?
 *            / \       / \
 *           E?  D?    C?  E?
 *
 * This updates pointers but not balance factors!
 */
IW_INLINE void avl_rotate(
  struct iwavl_node** const root_ptr,
  struct iwavl_node* const A, const int sign
  ) {
  struct iwavl_node* const B = iwavl_get_child(A, -sign);
  struct iwavl_node* const E = iwavl_get_child(B, +sign);
  struct iwavl_node* const P = iwavl_get_parent(A);

  avl_set_child(A, -sign, E);
  avl_set_parent(A, B);

  avl_set_child(B, +sign, A);
  avl_set_parent(B, P);

  if (E) {
    avl_set_parent(E, A);
  }

  avl_replace_child(root_ptr, P, A, B);
}

/*
 * Template for performing a double rotation ---
 *
 * sign > 0:  Rotate counterclockwise (left) rooted at B, then
 *		     clockwise (right) rooted at A:
 *
 *           P?            P?          P?
 *           |             |           |
 *           A             A           E
 *          / \           / \        /   \
 *         B   C?  =>    E   C? =>  B     A
 *        / \           / \        / \   / \
 *       D?  E         B   G?     D?  F?G?  C?
 *          / \       / \
 *         F?  G?    D?  F?
 *
 * (nodes marked with ? may not exist)
 *
 * sign < 0:  Rotate clockwise (right) rooted at B, then
 *		     counterclockwise (left) rooted at A:
 *
 *         P?          P?              P?
 *         |           |               |
 *         A           A               E
 *        / \         / \            /   \
 *       C?  B   =>  C?  E    =>    A     B
 *          / \         / \        / \   / \
 *         E   D?      G?  B      C?  G?F?  D?
 *        / \             / \
 *       G?  F?          F?  D?
 *
 * Returns a pointer to E and updates balance factors.  Except for those
 * two things, this function is equivalent to:
 *	avl_rotate(root_ptr, B, -sign);
 *	avl_rotate(root_ptr, A, +sign);
 *
 * See comment in avl_handle_subtree_growth() for explanation of balance
 * factor updates.
 */
IW_INLINE struct iwavl_node* avl_do_double_rotate(
  struct iwavl_node** const root_ptr,
  struct iwavl_node* const B,
  struct iwavl_node* const A, const int sign
  ) {
  struct iwavl_node* const E = iwavl_get_child(B, +sign);
  struct iwavl_node* const F = iwavl_get_child(E, -sign);
  struct iwavl_node* const G = iwavl_get_child(E, +sign);
  struct iwavl_node* const P = iwavl_get_parent(A);
  const int e = avl_get_balance_factor(E);

  avl_set_child(A, -sign, G);
  avl_set_parent_balance(A, E, ((sign * e >= 0) ? 0 : -e));

  avl_set_child(B, +sign, F);
  avl_set_parent_balance(B, E, ((sign * e <= 0) ? 0 : -e));

  avl_set_child(E, +sign, A);
  avl_set_child(E, -sign, B);
  avl_set_parent_balance(E, P, 0);

  if (G) {
    avl_set_parent(G, A);
  }

  if (F) {
    avl_set_parent(F, B);
  }

  avl_replace_child(root_ptr, P, A, E);

  return E;
}

/*
 * This function handles the growth of a subtree due to an insertion.
 *
 * @root_ptr
 *	Location of the tree's root pointer.
 *
 * @node
 *	A subtree that has increased in height by 1 due to an insertion.
 *
 * @parent
 *	Parent of @node; must not be 0.
 *
 * @sign
 *	-1 if @node is the left child of @parent;
 *	+1 if @node is the right child of @parent.
 *
 * This function will adjust @parent's balance factor, then do a (single
 * or double) rotation if necessary.  The return value will be %true if
 * the full AVL tree is now adequately balanced, or %false if the subtree
 * rooted at @parent is now adequately balanced but has increased in
 * height by 1, so the caller should continue up the tree.
 *
 * Note that if %false is returned, no rotation will have been done.
 * Indeed, a single node insertion cannot require that more than one
 * (single or double) rotation be done.
 */
IW_INLINE bool avl_handle_subtree_growth(
  struct iwavl_node** const root_ptr,
  struct iwavl_node* const  node,
  struct iwavl_node* const  parent,
  const int                 sign
  ) {
  int old_balance_factor, new_balance_factor;

  old_balance_factor = avl_get_balance_factor(parent);

  if (old_balance_factor == 0) {
    avl_adjust_balance_factor(parent, sign);
    /* @parent is still sufficiently balanced (-1 or +1
     * balance factor), but must have increased in height.
     * Continue up the tree.  */
    return false;
  }

  new_balance_factor = old_balance_factor + sign;

  if (new_balance_factor == 0) {
    avl_adjust_balance_factor(parent, sign);
    /* @parent is now perfectly balanced (0 balance factor).
     * It cannot have increased in height, so there is
     * nothing more to do.  */
    return true;
  }

  /* @parent is too left-heavy (new_balance_factor == -2) or
   * too right-heavy (new_balance_factor == +2).  */

  /* Test whether @node is left-heavy (-1 balance factor) or
   * right-heavy (+1 balance factor).
   * Note that it cannot be perfectly balanced (0 balance factor)
   * because here we are under the invariant that @node has
   * increased in height due to the insertion.  */
  if (sign * avl_get_balance_factor(node) > 0) {
    /* @node (B below) is heavy in the same direction @parent
     * (A below) is heavy.
     *
     * @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
     * The comment, diagram, and equations below assume sign < 0.
     * The other case is symmetric!
     * @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
     *
     * Do a clockwise rotation rooted at @parent (A below):
     *
     *           A              B
     *          / \           /   \
     *         B   C?  =>    D     A
     *        / \           / \   / \
     *       D   E?        F?  G?E?  C?
     *      / \
     *     F?  G?
     *
     * Before the rotation:
     *	balance(A) = -2
     *	balance(B) = -1
     * Let x = height(C).  Then:
     *	height(B) = x + 2
     *	height(D) = x + 1
     *	height(E) = x
     *	max(height(F), height(G)) = x.
     *
     * After the rotation:
     *	height(D) = max(height(F), height(G)) + 1
     *		  = x + 1
     *	height(A) = max(height(E), height(C)) + 1
     *		  = max(x, x) + 1 = x + 1
     *	balance(B) = 0
     *	balance(A) = 0
     */
    avl_rotate(root_ptr, parent, -sign);

    /* Equivalent to setting @parent's balance factor to 0.  */
    avl_adjust_balance_factor(parent, -sign); /* A */

    /* Equivalent to setting @node's balance factor to 0.  */
    avl_adjust_balance_factor(node, -sign);   /* B */
  } else {
    /* @node (B below) is heavy in the direction opposite
     * from the direction @parent (A below) is heavy.
     *
     * @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
     * The comment, diagram, and equations below assume sign < 0.
     * The other case is symmetric!
     * @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
     *
     * Do a counterblockwise rotation rooted at @node (B below),
     * then a clockwise rotation rooted at @parent (A below):
     *
     *           A             A           E
     *          / \           / \        /   \
     *         B   C?  =>    E   C? =>  B     A
     *        / \           / \        / \   / \
     *       D?  E         B   G?     D?  F?G?  C?
     *          / \       / \
     *         F?  G?    D?  F?
     *
     * Before the rotation:
     *	balance(A) = -2
     *	balance(B) = +1
     * Let x = height(C).  Then:
     *	height(B) = x + 2
     *	height(E) = x + 1
     *	height(D) = x
     *	max(height(F), height(G)) = x
     *
     * After both rotations:
     *	height(A) = max(height(G), height(C)) + 1
     *		  = x + 1
     *	balance(A) = balance(E{orig}) >= 0 ? 0 : -balance(E{orig})
     *	height(B) = max(height(D), height(F)) + 1
     *		  = x + 1
     *	balance(B) = balance(E{orig} <= 0) ? 0 : -balance(E{orig})
     *
     *	height(E) = x + 2
     *	balance(E) = 0
     */
    avl_do_double_rotate(root_ptr, node, parent, -sign);
  }

  /* Height after rotation is unchanged; nothing more to do.  */
  return true;
}

/* Rebalance the tree after insertion of the specified node.  */
void iwavl_rebalance_after_insert(
  struct iwavl_node **root_ptr,
  struct iwavl_node  *inserted
  ) {
  struct iwavl_node *node, *parent;
  bool done;

  inserted->left = 0;
  inserted->right = 0;

  node = inserted;

  /* Adjust balance factor of new node's parent.
   * No rotation will need to be done at this level.  */

  parent = iwavl_get_parent(node);
  if (!parent) {
    return;
  }

  if (node == parent->left) {
    avl_adjust_balance_factor(parent, -1);
  } else {
    avl_adjust_balance_factor(parent, +1);
  }

  if (avl_get_balance_factor(parent) == 0) {
    /* @parent did not change in height.  Nothing more to do.  */
    return;
  }

  /* The subtree rooted at @parent increased in height by 1.  */

  do {
    /* Adjust balance factor of next ancestor.  */

    node = parent;
    parent = iwavl_get_parent(node);
    if (!parent) {
      return;
    }

    /* The subtree rooted at @node has increased in height by 1.  */
    if (node == parent->left) {
      done = avl_handle_subtree_growth(root_ptr, node,
                                       parent, -1);
    } else {
      done = avl_handle_subtree_growth(root_ptr, node,
                                       parent, +1);
    }
  } while (!done);
}

/*
 * This function handles the shrinkage of a subtree due to a deletion.
 *
 * @root_ptr
 *	Location of the tree's root pointer.
 *
 * @parent
 *	A node in the tree, exactly one of whose subtrees has decreased
 *	in height by 1 due to a deletion.  (This includes the case where
 *	one of the child pointers has become 0, since we can consider
 *	the "0" subtree to have a height of 0.)
 *
 * @sign
 *	+1 if the left subtree of @parent has decreased in height by 1;
 *	-1 if the right subtree of @parent has decreased in height by 1.
 *
 * @left_deleted_ret
 *	If the return value is not 0, this will be set to %true if the
 *	left subtree of the returned node has decreased in height by 1,
 *	or %false if the right subtree of the returned node has decreased
 *	in height by 1.
 *
 * This function will adjust @parent's balance factor, then do a (single
 * or double) rotation if necessary.  The return value will be 0 if
 * the full AVL tree is now adequately balanced, or a pointer to the
 * parent of @parent if @parent is now adequately balanced but has
 * decreased in height by 1.  Also in the latter case, *left_deleted_ret
 * will be set.
 */
IW_INLINE struct iwavl_node* avl_handle_subtree_shrink(
  struct iwavl_node** const root_ptr,
  struct iwavl_node        *parent,
  const int                 sign,
  bool* const               left_deleted_ret
  ) {
  struct iwavl_node *node;
  int old_balance_factor, new_balance_factor;

  old_balance_factor = avl_get_balance_factor(parent);

  if (old_balance_factor == 0) {
    /* Prior to the deletion, the subtree rooted at
     * @parent was perfectly balanced.  It's now
     * unbalanced by 1, but that's okay and its height
     * hasn't changed.  Nothing more to do.  */
    avl_adjust_balance_factor(parent, sign);
    return 0;
  }

  new_balance_factor = old_balance_factor + sign;

  if (new_balance_factor == 0) {
    /* The subtree rooted at @parent is now perfectly
     * balanced, whereas before the deletion it was
     * unbalanced by 1.  Its height must have decreased
     * by 1.  No rotation is needed at this location,
     * but continue up the tree.  */
    avl_adjust_balance_factor(parent, sign);
    node = parent;
  } else {
    /* @parent is too left-heavy (new_balance_factor == -2) or
     * too right-heavy (new_balance_factor == +2).  */

    node = iwavl_get_child(parent, sign);

    /* The rotations below are similar to those done during
     * insertion (see avl_handle_subtree_growth()), so full
     * comments are not provided.  The only new case is the
     * one where @node has a balance factor of 0, and that is
     * commented.  */

    if (sign * avl_get_balance_factor(node) >= 0) {
      avl_rotate(root_ptr, parent, -sign);

      if (avl_get_balance_factor(node) == 0) {
        /*
         * @node (B below) is perfectly balanced.
         *
         * @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
         * The comment, diagram, and equations
         * below assume sign < 0.  The other case
         * is symmetric!
         * @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
         *
         * Do a clockwise rotation rooted at
         * @parent (A below):
         *
         *           A              B
         *          / \           /   \
         *         B   C?  =>    D     A
         *        / \           / \   / \
         *       D   E         F?  G?E   C?
         *      / \
         *     F?  G?
         *
         * Before the rotation:
         *	balance(A) = -2
         *	balance(B) =  0
         * Let x = height(C).  Then:
         *	height(B) = x + 2
         *	height(D) = x + 1
         *	height(E) = x + 1
         *	max(height(F), height(G)) = x.
         *
         * After the rotation:
         *	height(D) = max(height(F), height(G)) + 1
         *		  = x + 1
         *	height(A) = max(height(E), height(C)) + 1
         *		  = max(x + 1, x) + 1 = x + 2
         *	balance(A) = -1
         *	balance(B) = +1
         */

        /* A: -2 => -1 (sign < 0)
        * or +2 => +1 (sign > 0)
        * No change needed --- that's the same as
        * old_balance_factor.  */

        /* B: 0 => +1 (sign < 0)
         * or 0 => -1 (sign > 0)  */
        avl_adjust_balance_factor(node, -sign);

        /* Height is unchanged; nothing more to do.  */
        return 0;
      } else {
        avl_adjust_balance_factor(parent, -sign);
        avl_adjust_balance_factor(node, -sign);
      }
    } else {
      node = avl_do_double_rotate(root_ptr, node,
                                  parent, -sign);
    }
  }
  parent = iwavl_get_parent(node);
  if (parent) {
    *left_deleted_ret = (node == parent->left);
  }
  return parent;
}

/* Swaps node X, which must have 2 children, with its in-order successor, then
 * unlinks node X.  Returns the parent of X just before unlinking, without its
 * balance factor having been updated to account for the unlink.  */
IW_INLINE struct iwavl_node* avl_tree_swap_with_successor(
  struct iwavl_node **root_ptr,
  struct iwavl_node  *X,
  bool               *left_deleted_ret
  ) {
  struct iwavl_node *Y, *ret;

  Y = X->right;
  if (!Y->left) {
    /*
     *     P?           P?           P?
     *     |            |            |
     *     X            Y            Y
     *    / \          / \          / \
     *   A   Y    =>  A   X    =>  A   B?
     *      / \          / \
     *    (0)  B?      (0)  B?
     *
     * [ X unlinked, Y returned ]
     */
    ret = Y;
    *left_deleted_ret = false;
  } else {
    struct iwavl_node *Q;

    do {
      Q = Y;
      Y = Y->left;
    } while (Y->left);

    /*
     *     P?           P?           P?
     *     |            |            |
     *     X            Y            Y
     *    / \          / \          / \
     *   A   ...  =>  A  ...   =>  A  ...
     *       |            |            |
     *       Q            Q            Q
     *      /            /            /
     *     Y            X            B?
     *    / \          / \
     *  (0)  B?      (0)  B?
     *
     *
     * [ X unlinked, Q returned ]
     */

    Q->left = Y->right;
    if (Q->left) {
      avl_set_parent(Q->left, Q);
    }
    Y->right = X->right;
    avl_set_parent(X->right, Y);
    ret = Q;
    *left_deleted_ret = true;
  }

  Y->left = X->left;
  avl_set_parent(X->left, Y);

  Y->parent_balance = X->parent_balance;
  avl_replace_child(root_ptr, iwavl_get_parent(X), X, Y);

  return ret;
}

/*
 * Removes an item from the specified AVL tree.
 *
 * @root_ptr
 *	Location of the AVL tree's root pointer.  Indirection is needed
 *	because the root node may change if the tree needed to be rebalanced
 *	because of the deletion or if @node was the root node.
 *
 * @node
 *	Pointer to the `struct iwavl_node' embedded in the item to
 *	remove from the tree.
 *
 * Note: This function *only* removes the node and rebalances the tree.
 * It does not free any memory, nor does it do the equivalent of
 * iwavl_node_set_unlinked().
 */
void iwavl_remove(struct iwavl_node **root_ptr, struct iwavl_node *node) {
  struct iwavl_node *parent;
  bool left_deleted = false;

  if (node->left && node->right) {
    /* @node is fully internal, with two children.  Swap it
     * with its in-order successor (which must exist in the
     * right subtree of @node and can have, at most, a right
     * child), then unlink @node.  */
    parent = avl_tree_swap_with_successor(root_ptr, node,
                                          &left_deleted);
    /* @parent is now the parent of what was @node's in-order
     * successor.  It cannot be 0, since @node itself was
     * an ancestor of its in-order successor.
     * @left_deleted has been set to %true if @node's
     * in-order successor was the left child of @parent,
     * otherwise %false.  */
  } else {
    struct iwavl_node *child;

    /* @node is missing at least one child.  Unlink it.  Set
     * @parent to @node's parent, and set @left_deleted to
     * reflect which child of @parent @node was.  Or, if
     * @node was the root node, simply update the root node
     * and return.  */
    child = node->left ? node->left : node->right;
    parent = iwavl_get_parent(node);
    if (parent) {
      if (node == parent->left) {
        parent->left = child;
        left_deleted = true;
      } else {
        parent->right = child;
        left_deleted = false;
      }
      if (child) {
        avl_set_parent(child, parent);
      }
    } else {
      if (child) {
        avl_set_parent(child, parent);
      }
      *root_ptr = child;
      return;
    }
  }

  /* Rebalance the tree.  */
  do {
    if (left_deleted) {
      parent = avl_handle_subtree_shrink(root_ptr, parent,
                                         +1, &left_deleted);
    } else {
      parent = avl_handle_subtree_shrink(root_ptr, parent,
                                         -1, &left_deleted);
    }
  } while (parent);
}
